An arrester having the aforementioned configuration is disclosed, for example, in the article "Reliability and Application of Metal Oxide Surge Arrestors for Power Systems," by S. Tominaga et al, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-98, No. 3 (1979), in particular beginning with page 809. In the Tominaga et al arrester, a linear potential-distribution along its active portion and a good dielectric strength are achieved by means of an electrically conducting shield which is connected to an element conducting the high voltage and extends along the arrester elements, as well as by means of screening rings. Considerable costs are associated with the construction of arresters of this type. Furthermore, the shape and dimensions of the screening and controlling bodies can be determined only with the aid of relatively complicated measurements and computation procedures. High manufacturing costs must accordingly be expected, especially in cases involving the building of arresters in small series.